Maple for PlanetPhysics
MapleForPlanetPhysics
2005-09-02 12:26:13
2005-09-03 01:01:53
Definition
% this is the default PlanetMath preamble. as your knowledge
% of TeX increases, you will probably want to edit this, but
% it should be fine as is for beginners.
% almost certainly you want these
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
% used for TeXing text within eps files
%\usepackage{psfrag}
% need this for including graphics (\includegraphics)
\usepackage{graphicx}
% for neatly defining theorems and propositions
%\usepackage{amsthm}
% making logically defined graphics
%\usepackage{xypic}
% there are many more packages, add them here as you need them
\usepackage{maplestd2e}
% define commands here
\begin{maplelatex}\mapleinline{inert}{2d}{%[poincare, generate_ic, zoom, hamilton_eqs]}{
$[{\it poincare},{\it generate\_ic},{\it zoom},{\it hamilton\_eqs}\\
\mbox{}]$}
\end{maplelatex}\begin{maplelatex}\begin{Maple Heading 1}{\textbf{The Toda Hamiltonian}}\end{Maple Heading 1}
\end{maplelatex}
\begin{maplelatex}\begin{Maple Normal}{\textbf{Reference: }A.J. Lichtenberg and M.A. Lieberman, "Regular and Stochastic Motion", \textit{Applied Mathematical Sciences} 38 (New York: Springer Verlag, 1994).}\end{Maple Normal}
\textbf{H := 1/2*(p1\symbol{94}2 + p2\symbol{94}2) + 1/24*(exp(2*q2+2*sqrt(3)*q1) + exp(2*q2-2*sqrt(3)*q1) + exp(-4*q2))-1/8;}\end{maplelatex}
\mapleresult
\begin{maplelatex}\mapleinline{inert}{2d}{%H := p1^2/2+p2^2/2+1/24*exp(2*q2+2*3^(1/2)*q1)+1/24*exp(2*q2-2*3^(1/2)*q1)+1/24*exp(-4*q2)-1/8}{
$H\, := \,1/2\,{{\it p1}}^{2}+1/2\,{{\it p2}}^{2}+1/24\,{e^{2\,{\it q2}+2\,\sqrt {3}{\it q1}}}\\
\mbox{}+1/24\,{e^{2\,{\it q2}-2\,\sqrt {3}{\it q1}}}+1/24\,{e^{-4\,{\it q2}}}-1/8$}
\end{maplelatex}\begin{mapleinput}
\mapleinline{active}{1d}{\textbf{H, t=-150..150, \{[0,.1,1.4,.1,0]\}:}}{}
\end{mapleinput}
\begin{mapleinput}
\mapleinline{active}{1d}{\begin{Maple Normal}{\textbf{poincare(%, stepsize=.05,iterations=5); }(12 sec.)}\end{Maple Normal}
}{}
\end{mapleinput}
\mapleresult
\begin{maplelatex}\mapleinline{inert}{2d}{%_____________________________________________________}{
\[{\it \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}\]}
\end{maplelatex}\begin{maplelatex}\mapleinline{inert}{2d}{%`H = .99005020`, ` Initial conditions:`, t = 0, p1 = .1, p2 = 1.4, q1 = .1, q2 = 0}{
$\mbox {{\tt `H = .99005020`}},\,\mbox {{\tt ` Initial conditions:`}},\,t=0,\,{\it p1}= 0.1,\,{\it p2}= 1.4,\,{\it q1}= 0.1,\,{\it q2}=0$}
\end{maplelatex}\begin{maplelatex}\mapleinline{inert}{2d}{%`Number of points found crossing the (p1,q1) plane: 127`}{
$\mbox {{\tt `Number of points found crossing the (p1,q1) plane: 127`}}$}
\end{maplelatex}\begin{maplelatex}\mapleinline{inert}{2d}{%`Maximum H deviation : .5740000000e-5 %`}{
$\mbox {{\tt `Maximum H deviation : .5740000000e-5 \%`}}$}
\end{maplelatex}\begin{maplelatex}\mapleinline{inert}{2d}{%_____________________________________________________}{
\[{\it \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}\]}
\end{maplelatex}\begin{maplelatex}\mapleinline{inert}{2d}{%`Time consumed: 12 seconds`}{
$\mbox {{\tt `Time consumed: 12 seconds`}}$}
\end{maplelatex}
%\mapleplot{poly.eps}
\medskip
\begin{figure}
\includegraphics{poincareplot1.eps}
\end{figure}
\medskip
\begin{maplelatex}\begin{Maple Normal}{Figure 1.a. shows a 2-D surface-of-section (2PS) over the q2=0 plane, with 127 intersection points lying on smooth curves.
}\end{Maple Normal}
\end{maplelatex}\begin{mapleinput}
\mapleinline{active}{1d}{\begin{Maple Normal}{\textbf{poincare(%%,stepsize=.05,iterations=5,scene=[p2,q2]); }(13 sec.)}\end{Maple Normal}
}{}
\end{mapleinput}